Multi-antenna techniques can significantly increase the data rates and reliability of a wireless communication system. The performance is in particular improved if both the transmitter and the receiver are equipped with multiple antennas, which results in a multiple-input multiple-output (MIMO) communication channel. Such systems and/or related techniques are commonly referred to as MIMO.
The 3GPP long term evolution (LTE) standard is currently evolving with enhanced MIMO support. A core component in LTE is the support of MIMO antenna deployments and MIMO related techniques. Currently LTE-Advanced supports an 8-layer spatial multiplexing mode for up to 16 transmit antennas with channel dependent precoding, and in LTE Rel. 14 support for up to 32 transmit antennas will be added. The spatial multiplexing mode is aimed for high data rates in favorable channel conditions. An illustration of the spatial multiplexing operation is provided in FIG. 1.
As seen, the information carrying symbol vector s 10 is multiplied by an NT×r precoder matrix W, 12 which serves to distribute the transmit energy in a subspace of the NT (corresponding to NT antenna ports 14) dimensional vector space. The precoder matrix 12 is typically selected from a codebook of possible precoder matrices, and typically indicated by means of a precoder matrix indicator (PMI), which specifies a unique precoder matrix in the codebook for a given number of symbol streams. The r symbols in s 10 each correspond to a layer and r is referred to as the transmission rank. In this way, spatial multiplexing is achieved since multiple symbols can be transmitted simultaneously over the same time/frequency resource element (TFRE). The number of symbols r is typically adapted to suit the current channel properties.
LTE uses OFDM in the downlink (and DFT precoded OFDM in the uplink) and hence the received NR×1 vector yn for a certain TFRE on subcarrier n (or alternatively data TFRE number n) is thus modeled byyn=HnWsn+en  Equation 1
where en is a noise/interference vector obtained as realizations of a random process. The precoder W can be a wideband precoder, which is constant over frequency, or frequency selective.
The precoder matrix W 12 is often chosen to match the characteristics of the NR×NT MIMO channel matrix Hn, resulting in so-called channel dependent precoding. This is also commonly referred to as closed-loop precoding and essentially strives for focusing the transmit energy into a subspace which is strong in the sense of conveying much of the transmitted energy to the wireless device. In addition, the precoder matrix 12 may also be selected to strive for orthogonalizing the channel, meaning that after proper linear equalization at the wireless device, the inter-layer interference is reduced.
One example method for a wireless device to select a precoder matrix W 12 can be to select the Wk that maximizes the Frobenius norm of the hypothesized equivalent channel:
                              max          k                ⁢                  ||                                                    H                ^                            n                        ⁢                          W              k                                ⁢                      ||            F            2                                              Equation        ⁢                                  ⁢        2            Where                Ĥn is a channel estimate, possibly derived from CSI-RS as described below.        Wk is a hypothesized precoder matrix with index k.        ĤnWk is the hypothesized equivalent channel        
In closed-loop precoding for the LTE downlink, the wireless device transmits, based on channel measurements in the forward link (downlink), recommendations to the base station, e.g., eNodeB (eNB) of a suitable precoder to use. The base station configures the wireless device to provide feedback according to the wireless device's transmission mode, and may transmit CSI-RS and configure the wireless device to use measurements of CSI-RS to feedback recommended precoding matrices that the wireless device selects from a codebook. A single precoder that is supposed to cover a large bandwidth (wideband precoding) may be fed back. It may also be beneficial to match the frequency variations of the channel and instead feedback a frequency-selective precoding report, e.g., several precoders, one per subband. This is an example of the more general case of channel state information (CSI) feedback, which also encompasses feeding back other information that recommended precoders to assist the eNodeB in subsequent transmissions to the wireless device. Such other information may include channel quality indicators (CQIs) as well as transmission rank indicator (RI).
With regards to CSI feedback, a subband is defined as a number of adjacent PRB pairs. In LTE, the subband size (i.e., the number of adjacent PRB pairs) depends on the system bandwidth, whether CSI reporting is configured to be periodic or aperiodic, and feedback type (i.e., whether higher layer configured feedback or wireless device-selected subband feedback is configured). An example illustrating the difference between subband and wideband is shown in FIG. 2. In the example, the subband consists of 6 adjacent PRBs. Note that only 2 subbands are shown in FIG. 2 for simplicity of illustration. Generally, all the PRB pairs in the system bandwidth are divided into different subband where each subband consists of a fixed number of PRB pairs. In contrast, wideband involves all the PRB pairs in the system bandwidth. As mentioned above, a wireless device may feedback a single precoder that takes into account the measurements from all PRB pairs in the system bandwidth if it is configured to report wideband PMI by the base station. Alternatively, if the wireless device is configured to report subband PMI, a wireless device may feedback multiple precoders with one precoder per subband. In addition, to the subband precoders, the wireless device may also feedback the wideband PMI.
In LTE, two types of subband feedback types are possible for PUSCH CSI reporting: (1) higher layer configured subband feedback and (2) wireless device selected subband feedback. With higher layer configured subband feedback, the wireless device may feedback PMI and/or CQI for each of the subbands. The subband size in terms of the number of PRB pairs for higher layer configured subband feedback is a function of system bandwidth and is listed in Table 1. With wireless device selected subband feedback, the wireless device only feeds back PMI and/or CQI for a selected number of subbands out of all the subbands in the system bandwidth. The subband size in terms of the number of PRB pairs and the number of subbands to be fed back are a function of the system bandwidth and are listed in Table 2.
TABLE 1System BandwidthSubband SizeNRB(ksub)6-7NA 8-10411-26427-636 64-1108
TABLE 2System BandwidthNRBDLSubband Size k (RBs)Number of Subbands6-7NANA 8-102111-262327-6335 64-11046
Given the CSI feedback from the wireless device, the base station determines the transmission parameters it wishes to use to transmit to the wireless device, including the precoding matrix, transmission rank, and modulation and coding state (MCS). These transmission parameters may differ from the recommendations the wireless device makes. Therefore, a rank indicator and MCS may be signaled in downlink control information (DCI), and the precoding matrix can be signaled in DCI or the base station can transmit a demodulation reference signal from which the equivalent channel can be measured. The transmission rank, and thus the number of spatially multiplexed layers, is reflected in the number of columns of the precoder W. For efficient performance, it is important that a transmission rank that matches the channel properties is selected.
In LTE Release-10, a new reference symbol sequence was introduced for the intent to estimate downlink channel state information, the CSI-RS. The CSI-RS provides several advantages over basing the CSI feedback on the common reference symbols (CRS) which were used, for that purpose, in Releases 8-9. Firstly, the CSI-RS is not used for demodulation of the data signal, and thus does not require the same density (i.e., the overhead of the CSI-RS is substantially less). Secondly, CSI-RS provides a much more flexible means to configure CSI feedback measurements (e.g., which CSI-RS resource to measure on can be configured in a wireless device specific manner).
By measuring a CSI-RS transmitted from the base station, a wireless device can estimate the effective channel the CSI-RS is traversing including the radio propagation channel and antenna gains. In more mathematical rigor this implies that if a known CSI-RS signal x is transmitted, a wireless device can estimate the coupling between the transmitted signal and the received signal (i.e., the effective channel). Hence if no virtualization is performed in the transmission, the received signal Y can be expressed asy=Hx+e  Equation 3
and the wireless device can estimate the effective channel H.
Up to eight CSI-RS ports can be configured in LTE Rel-10, that is, the wireless device can estimate the channel from up to eight transmit antenna ports. In LTE Release 13, the number of CSI-RS ports that can be configured is extended to up to sixteen ports. In LTE Release 14, supporting up to 32 CSI-RS ports is under consideration.
Related to CSI-RS is the concept of zero-power CSI-RS resources (also known as a muted CSI-RS) that are configured just as regular CSI-RS resources, so that a wireless device knows that the data transmission is mapped around those resources. The intent of the zero-power CSI-RS resources is to enable the network to mute the transmission on the corresponding resources in order to boost the signal-to-interference-plus-noise ratio (SINR) of a corresponding non-zero power CSI-RS, possibly transmitted in a neighbor cell/transmission point. For Rel-11 of LTE a special zero-power CSI-RS was introduced that a wireless device is mandated to use for measuring interference plus noise. A wireless device can assume that the serving eNB is not transmitting on the zero-power CSI-RS resource, and the received power can therefore be used as a measure of the interference plus noise.
Based on a specified CSI-RS resource and on an interference measurement configuration (e.g., a zero-power CSI-RS resource), the wireless device can estimate the effective channel and noise plus interference, and consequently also determine the rank, precoding matrix, and MCS to recommend to best match the particular channel
In the previous description of CSI-RS, so called non-precoded CSI-RS was assumed. Meaning that one CSI-RS antenna port mapped to a single antenna element or antenna subarray of the antenna array. The CSI-RS in this case are then intended to be cell-specific, i.e., broadcasted over the entire cell coverage area. However, in LTE Rel. 13, a new type of CSI-RS transmitting scheme was introduced, so called beamformed (or precoded) CSI-RS. These CSI-RS are intended to be UE-specific instead of cell-specific, so that each wireless device is assigned a dedicated CSI-RS resource. Such beamformed CSI-RS typically contain much fewer ports than non-precoded CSI-RS and correspond to more narrow beams, as they are typically only intended to cover the wireless device of interest and not the entire cell coverage area. Using LTE terminology, non-precoded CSI-RS transmission schemes are denoted “Class A eMIMO-Type” while beamformed CSI-RS transmission schemes are denoted “Class B eMIMO-Type”.
A problem with using the Class B approach is that the eNB needs to know how it should beamform the CSI-RS to the UE, i.e. in which direction to steer the beam. To solve this problem, a typical approach is to use so called Hybrid Class A/B operation, where in a first step a Class A CSI-RS with many antenna ports is transmitted by the eNB and a PMI report from a large dimension codebook is fed back by the wireless device to the eNB. The indicated precoder in the PMI thus indicates the best beam direction for the UE. In subsequent steps, the eNB transmits a Class B CSI-RS with few antenna ports to the UE, where the beamforming of the CSI-RS is based on the reported precoder in the Class A report. The eNB will typically transmit a Class A CSI-RS at certain intervals (e.g. with a periodicity 10-20 times larger than the Class B CSI-RS) in order to assure that the UEs desired beam direction has not changed.
Embodiments may be used with two dimensional antenna arrays and some of the presented embodiments use such antennas. Such antenna arrays may be (partly) described by the number of antenna columns corresponding to the horizontal dimension Nh, the number of antenna rows corresponding to the vertical dimension Nv and the number of dimensions corresponding to different polarizations Np. The total number of antennas is thus N=NhNvNp. It should be pointed out that the concept of an antenna is non-limiting in the sense that it can refer to any virtualization (e.g., linear mapping) of the physical antenna elements. For example, pairs of physical sub-elements could be fed the same signal, and hence share the same virtualized antenna port.
An example of a 4×4 (i.e. four rows by four columns) array with cross-polarized antenna elements is shown in FIG. 3.
Precoding may be interpreted as multiplying the signal with different beamforming weights for each antenna prior to transmission. A typical approach is to tailor the precoder to the antenna form factor, i.e. taking into account Nh, Nv, and Np when designing the precoder codebook. A common type of precoding is to use a DFT-precoder, where the precoder vector used to precode a single-layer transmission using a single-polarized uniform linear array (ULA) with N1 antennas is defined as
                                          w                          1              ⁢              D                                ⁡                      (                          l              ,                              N                1                            ,                              O                1                                      )                          =                              1                                          N                1                                              ⁡                      [                                                                                e                                          j                      ⁢                                                                                          ⁢                      2                      ⁢                                              π                        ·                        0                        ·                                                  1                                                                                    O                              1                                                        ⁢                                                          N                              1                                                                                                                                                                                                                                            e                                          j                      ⁢                                                                                          ⁢                      2                      ⁢                                              π                        ·                        1                        ·                                                  1                                                                                    O                              1                                                        ⁢                                                          N                              1                                                                                                                                                                                                                        ⋮                                                                                                  e                                          j                      ⁢                                                                                          ⁢                      2                      ⁢                                              π                        ·                                                  (                                                                                    N                              1                                                        -                            1                                                    )                                                ·                                                  1                                                                                    O                              1                                                        ⁢                                                          N                              1                                                                                                                                                                                                ]                                              Equation        ⁢                                  ⁢        4            
where l=0, 1, . . . O1N1−1 is the precoder index and O1 is an integer oversampling factor. A precoder for a dual-polarized uniform linear array (ULA) with N1 antennas per polarization (and so 2N1 antennas in total) can be similarly defined as
                                          w                                          1                ⁢                D                            ,              DP                                ⁡                      (                          l              ,                              N                1                            ,                              O                1                                      )                          =                              [                                                                                                      w                                              1                        ⁢                        D                                                              ⁡                                          (                      l                      )                                                                                                                                                              e                                              j                        ⁢                                                                                                  ⁢                        ϕ                                                              ⁢                                                                  w                                                  1                          ⁢                          D                                                                    ⁡                                              (                        l                        )                                                                                                                  ]                    =                                    [                                                                                                                  w                                                  1                          ⁢                          D                                                                    ⁡                                              (                        l                        )                                                                                                  0                                                                                        0                                                                                                      w                                                  1                          ⁢                          D                                                                    ⁡                                              (                        l                        )                                                                                                        ]                        ⁡                          [                                                                    1                                                                                                              e                                              j                        ⁢                                                                                                  ⁢                        ϕ                                                                                                        ]                                                          Equation        ⁢                                  ⁢        5            
where ejϕ is a co-phasing factor between the two polarizations that may for instance be selected from a QPSK alphabet
  ϕ  ∈            {              0        ,                  π          2                ,        π        ,                              3            ⁢            π                    2                    }        .  
A corresponding precoder vector for a two-dimensional uniform planar arrays (UPA) with N1×N2 antennas can be created by taking the Kronecker product of two precoder vectors as w2D(l,m)=w1D(l, N1, O1)⊗w1D(m, N2, O2), where O2 is an integer oversampling factor in the N2 dimension. Each precoder w2D(l,m) forms a 2D DFT beam, all the precoders {w2D(l,m), l=0, . . . , N1O1−1; m=0, . . . , N2O2−1} form a grid of DFT beams. An example is shown in FIG. 4, where (N1, N2)=(4,2) and (O1, O2)=(4,4). Each of the grid of DFT beams points to a spatial direction which can be described by a joint direction in azimuth and elevation. Throughout the following sections, the terms ‘DFT beams’ and ‘DFT precoders’ are used interchangeably.
More generally, a beam with an index pair (l,m) can be identified by the direction in which the greatest energy is transmitted when precoding weights w2D(l,m) are used in the transmission. Also, a magnitude taper can be used with DFT beams to lower the beam's sidelobes, the beam pattern at directions away from the main beam. A 1D DFT precoder along N1 and N2 dimensions with magnitude tapering can be expressed as
                    w                  1          ⁢          D                    ⁡              (                  l          ,                      N            1                    ,                      O            1                    ,          β                )              =                  1                              N            1                              ⁡              [                                                                              β                  0                                ⁢                                  e                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                                          π                      ·                      0                      ·                                              1                                                                              O                            1                                                    ⁢                                                      N                            1                                                                                                                                                                                                                                        β                  1                                ⁢                                  e                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                                          π                      ·                      1                      ·                                              1                                                                              O                            1                                                    ⁢                                                      N                            1                                                                                                                                                                                                      ⋮                                                                                            β                                                            N                      1                                        -                    1                                                  ⁢                                  e                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                                          π                      ·                                              (                                                                              N                            1                                                    -                          1                                                )                                            ·                                              1                                                                              O                            1                                                    ⁢                                                      N                            1                                                                                                                                                                                  ]              ,                    w                  1          ⁢          D                    ⁡              (                  m          ,                      N            2                    ,                      O            2                    ,          γ                )              =                  1                              N            2                              ⁡              [                                                                              γ                  0                                ⁢                                  e                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                                          π                      ·                      0                      ·                                              m                                                                              O                            2                                                    ⁢                                                      N                            2                                                                                                                                                                                                                                        γ                  1                                ⁢                                  e                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                                          π                      ·                      1                      ·                                              m                                                                              O                            2                                                    ⁢                                                      N                            2                                                                                                                                                                                                      ⋮                                                                                            γ                                                            N                      2                                        -                    1                                                  ⁢                                  e                                      j                    ⁢                                                                                  ⁢                    2                    ⁢                                          π                      ·                                              (                                                                              N                            2                                                    -                          1                                                )                                            ·                                              m                                                                              O                            2                                                    ⁢                                                      N                            2                                                                                                                                                                                  ]            
Where 0<βi, γk≤1 (i=0, 1, . . . , N1−1; k=0, 1, . . . , N2−1) are amplitude scaling factors. βi=1, γk=1 (i=0, 1, . . . , N1−1; k=0, 1, . . . , N2−1) correspond to no tapering. DFT beams (with or without a magnitude taper) have a linear phase shift between elements along each of the two dimensions. Without loss of generality, one can assume that the elements of w(l,m) are ordered according to w(l,m)=w1D(l, N1, O1, β)⊗w1D(m, N2, O2, γ) such that adjacent elements correspond to adjacent antenna elements along dimension N2, and elements of w(l,m) spaced N2 apart correspond to adjacent antenna elements along dimension N1. Then the phase shift between two elements ws1 (l,m) and ws2 (l,m) of w(l,m) can be expressed as:
            w              s        2              ⁡          (              l        ,        m            )        =                    w                  s          1                    ⁡              (                  l          ,          m                )              ·          (                        α                      s            2                                    α                      s            1                              )        ·          e              j        ⁢                                  ⁢        2        ⁢                  π          ⁡                      (                                                            (                                                            k                      1                                        -                                          i                      1                                                        )                                ⁢                                  Δ                  1                                            +                                                (                                                            k                      2                                        -                                          i                      2                                                        )                                ⁢                                  Δ                  2                                                      )                              
Where
s1=iiN2+i2 and s2=k1N2+k2 (with 0≤i2<N2, 0≤i1≤N1, 0≤k2<N2, and 0≤k1<N1) are integers identifying two entries of the beam w(l,m) so that (i1, i2) indicates to a first entry of beam w(l,m) that is mapped to a first antenna element (or port) and (k1, k2) indicates to a second entry of beam w(l,m) that is mapped to a second antenna element (or port).
αs1=βi1γi2 and αs2=βk1γk2 are real numbers. αj≠1 (i=s1, s2) if magnitude tapering is used; otherwise αi=1.
      Δ    1    =      1                  O        1            ⁢              N        1            is a phase stint corresponding to a direction along an axis, e.g. the horizontal axis (‘azimuth’)
      Δ    2    =      m                  O        2            ⁢              N        2            is a phase shift corresponding to direction along an axis, e.g. the vertical axis (‘elevation’)
Therefore a kth beam d(k) formed with precoder w(lk, mk) can also be referred to by the corresponding precoder w(lk, mk), i.e. d(k)=w(lk, mk). Thus a beam d(k) can be described as a set of complex numbers, each element of the set being characterized by at least one complex phase shift such that an element of the beam is related to any other element of the beam where dn(k)=di(k)αi,nej2π(PΔ1,k+qΔ2,k)=di(k)αi,n(ej2π(PΔ1,k)p(ej2π(PΔ2,k)q, where di(k) is the ith element of a beam d(k), αi,n is a real number corresponding to the ith and nth elements of the beam d(k); p and q are integers; and Δ1,k and Δ2,k are real numbers corresponding to a beam with index pair (lk, mk) that determine the complex phase shifts ej2πΔ1,k and ej2πΔ2,k, respectively. Index pair (lk, mk) corresponds to a direction of arrival or departure of a plane wave when beam d(k) is used for transmission or reception in a UPA or ULA. A beam d(k) can be identified with a single index k where=lk+N1O1mk, i.e, along vertical or N2 dimension first, or alternatively k=N2O2lk+mk, i.e. along horizontal or N1 dimension first.
An example of precoder elements of a beam w(l,m) to antenna ports mapping is shown in FIG. 5, where a single polarization 2D antenna with (N1,N2)=(4,2) is illustrated. wi(l,m) is applied on the transmit (Tx) signal to port i (i=1, 2, . . . , 8). There is a constant phase shift between any two precoder elements associated with two adjacent antenna ports along each dimension. For example, with Δ2 defined as above, the phase shift between w1(l,m) and w2(l,m) is ej2πΔ2, which is the same as the phase shift between w7(l,m) and w8(l,m). Similarly, with Δ1 defined as above, the phase shift between w2(l,m) and w4(l,m) is ej2πΔ1, which is the same as the phase shift between w5(l,m) and w7(l,m).
Extending the precoder for a dual-polarized ULA may then be done as
                                                                                          w                                                            2                      ⁢                      D                                        ,                    DP                                                  ⁡                                  (                                      l                    ,                    m                    ,                    ϕ                                    )                                            =                                                                    [                                                                                            1                                                                                                                                                  e                                                          j                              ⁢                                                                                                                          ⁢                              ϕ                                                                                                                                            ]                                    ⊗                                                            w                                              2                        ⁢                        D                                                              ⁡                                          (                                              l                        ,                        m                                            )                                                                      =                                  [                                                                                                                                          w                                                          2                              ⁢                              D                                                                                ⁡                                                      (                                                          l                              ,                              m                                                        )                                                                                                                                                                                                                    e                                                          j                              ⁢                                                                                                                          ⁢                              ϕ                                                                                ⁢                                                                                    w                                                              2                                ⁢                                D                                                                                      ⁡                                                          (                                                              l                                ,                                m                                                            )                                                                                                                                                            ]                                                                                                        =                                                [                                                                                                                                          w                                                          2                              ⁢                              D                                                                                ⁡                                                      (                                                          l                              ,                              m                                                        )                                                                                                                      0                                                                                                            0                                                                                                                          w                                                          2                              ⁢                              D                                                                                ⁡                                                      (                                                          l                              ,                              m                                                        )                                                                                                                                ]                                ⁡                                  [                                                                                    1                                                                                                                                      e                                                      j                            ⁢                                                                                                                  ⁢                            ϕ                                                                                                                                ]                                                                                        Equation        ⁢                                  ⁢        6            
A precoder matrix w2D,DP for multi-layer transmission may be created by appending columns of DFT precoder vectors asW2D,DP(R)=[w2D,DP(l1,m1,ϕ1)w2D,DP(l2,m2,ϕ2) . . . w2D,DP(lR,mR,ϕR)]
where R is the number of transmission layers, i.e. the transmission rank. In a special case for a rank-2 DFT precoder, m1=m2=m and l1=l2=1, we have
                                                                                          W                                                            2                      ⁢                      D                                        ,                    DP                                                        (                    2                    )                                                  ⁡                                  (                                      l                    ,                    m                    ,                                          ϕ                      1                                        ,                                          ϕ                      2                                                        )                                            =                            ⁢                              [                                                                                                                              w                                                                                    2                              ⁢                              D                                                        ,                            DP                                                                          ⁡                                                  (                                                      l                            ,                            m                            ,                                                          ϕ                              1                                                                                )                                                                                                                                                              w                                                                                    2                              ⁢                              D                                                        ,                            DP                                                                          ⁡                                                  (                                                      l                            ,                            m                            ,                                                          ϕ                              2                                                                                )                                                                                                                    ]                                                                                        =                            ⁢                                                [                                                                                                                                          w                                                          2                              ⁢                              D                                                                                ⁡                                                      (                                                          l                              ,                              m                                                        )                                                                                                                      0                                                                                                            0                                                                                                                          w                                                          2                              ⁢                              D                                                                                ⁡                                                      (                                                          l                              ,                              m                                                        )                                                                                                                                ]                                ⁡                                  [                                                                                    1                                                                    1                                                                                                                                      e                                                      j                            ⁢                                                                                                                  ⁢                                                          ϕ                              1                                                                                                                                                                            e                                                      j                            ⁢                                                                                                                  ⁢                                                          ϕ                              2                                                                                                                                                            ]                                                                                        Equation        ⁢                                  ⁢        7            
For each rank, all the precoder candidates form a ‘precoder codebook’ or a ‘codebook’. A wireless device can first determine the rank of the estimated downlink wideband channel based CSI-RS. After the rank is identified, for each subband the wireless device then searches through all the precoder candidates in a codebook for the determined rank to find the best precoder for the subband. For example, in case of rank=1, the wireless device would search through w2D,DP(k,l,ϕ) for all the possible (k,l,ϕ) values. In case of rank=2, the wireless device would search through W2D,DP(2)(k,l,ϕ1,ϕ2) for all the possible (k,l,ϕ1,ϕ2) values.
With multi-user MIMO, two or more users in the same cell are co-scheduled on the same time-frequency resource. That is, two or more independent data streams are transmitted to different wireless devices at the same time, and the spatial domain is used to separate the respective streams. By transmitting several streams simultaneously, the capacity of the system can be increased. This however, comes at the cost of reducing the SINR per stream, as the power has to be shared between streams and the streams will cause interference to each other.
When increasing the antenna array size, the increased beamforming gain will lead to higher SINR, however, as the user throughput depends only logarithmically on the SINR (for large SINRs), it is instead beneficial to trade the gains in SINR for a multiplexing gain, which increases linearly with the number of multiplexed users.
Accurate CSI is required in order to perform appropriate nullforming between co-scheduled users. In the current LTE Rel.13 standard, no special CSI mode for MU-MIMO exists and thus, MU-MIMO scheduling and precoder construction has to be based on the existing CSI reporting designed for single-user MIMO (that is, a PMI indicating a DFT-based precoder, a RI and a CQI). This may prove quite challenging for MU-MIMO, as the reported precoder only contains information about the strongest channel direction for a user and may thus not contain enough information to do proper nullforming, which may lead to a large amount of interference between co-scheduled users, reducing the benefit of MU-MIMO.
Advanced codebooks, for Class A operation, comprising precoders with multiple beams have been shown to improve MU-MIMO performance due to enhanced nullforming capabilities. Such multi-beam precoders may be defined as follows. We first define DN as a size N×N DFT matrix, i.e. the elements of DN are defined as
            [              D        N            ]              k      ,      l        =            1              N              ⁢                  e                              j            ⁢                                                  ⁢            2            ⁢            π            ⁢                                                  ⁢            kl                    N                    .      Further we define RN(q)=diag
  (      [                                        e                          j              ⁢                                                          ⁢              2              ⁢                                                          ⁢                              π                ·                0                ·                                  q                  N                                                                                          e                          j              ⁢                                                          ⁢              2              ⁢                                                          ⁢                              π                ·                1                ·                                  q                  N                                                                              …                                      e                          j              ⁢                                                          ⁢              2              ⁢                                                          ⁢                              π                ·                                  (                                      N                    -                    1                                    )                                ·                                  q                  N                                                                          ]    )to be a size N×N rotation matrix, defined for 0≤q<1. Multiplying DN with RN(q) from the left creates a rotated
DFT matrix with entries
            [                                    R            N                    ⁡                      (            q            )                          ⁢                  D          N                    ]              k      ,      l        =            1              N              ⁢                  e                              j            ⁢                                                  ⁢            2            ⁢            π            ⁢                                                  ⁢                          k              ⁡                              (                                  l                  +                  q                                )                                              N                    .      The rotated DFT matrix RN(q)DN=[d1 d2 . . . dN] consist of normalized orthogonal column vectors {di}i=1N which furthermore span the vector space N. That is, the columns of RN(q)DN, for any q, is an orthonormal basis of N.
We begin with extending the (rotated) DFT matrices that were appropriate transforms for a single-polarized ULA as discussed above to also fit the more general case of dual-polarized 2D uniform planar arrays (UPAs).
We define a rotated 2D DFT matrix as DNV,NH(qV,qH)=(RNH(qH)DNH)⊗(RNV(qV)DNV)=[d1 d2 . . . dNVNH]. The columns {di}i=1NDP of DNV,NH(qV, qH) constitutes an orthonormal basis of the vector space NVNH. Such a column di is henceforth denoted a (DFT) beam, and we note that it fulfills the earlier definition of a beam given above.
Consider now a dual-polarized UPA, where the channel matrix H=[Hpol1 Hpol2]. Create a dual-polarized beam space transformation matrix
            B                        N          V                ,                  N          H                      ⁡          (                        q          V                ,                  q          H                    )        =                    I        2            ⊗                        D                                    N              V                        ,                          N              H                                      ⁡                  (                                    q              V                        ,                          q              H                                )                      =                  [                                                                              D                                                            N                      V                                        ,                                          N                      H                                                                      ⁡                                  (                                                            q                      V                                        ,                                          q                      H                                                        )                                                                    0                                                          0                                                                        D                                                            N                      V                                        ,                                          N                      H                                                                      ⁡                                  (                                                            q                      V                                        ,                                          q                      H                                                        )                                                                    ]            =                                             [                                                                                d                    1                                                                                        d                    2                                                                    …                                                                      d                                                                  N                        V                                            ⁢                                              N                        H                                                                                                              0                                                  0                                                  …                                                  0                                                                              0                                                  0                                                  …                                                  0                                                                      d                    1                                                                                        d                    2                                                                    …                                                                      d                                                                  N                        V                                            ⁢                                              N                        H                                                                                                                  ]                    =                                                                 [                                                                                                    b                        1                                                                                                            b                        2                                                                                    …                                                                                      b                                                  2                          ⁢                                                      N                            V                                                    ⁢                                                      N                            H                                                                                                                                              ]                            ⁢                                                          .                                          The columns {di}i=12NVNH(qV, qH) constitutes an orthonormal basis of the vector space 2NVNH. Such a column bi is henceforth denoted a single-polarized beam (SP-beam) as it is constructed by a beam d transmitted on a single polarization
      (                  i        .        e        .                                  ⁢        b            =                                    [                                                            d                                                                              0                                                      ]                    ⁢                                          ⁢          or          ⁢                                          ⁢          b                =                  [                                                    0                                                                    d                                              ]                      )    .We also introduce a notation dual-polarized beam to refer to a beam transmitted on both polarizations (co-phased with an (arbitrary) co-phasing factor ejα,
                    i        .        e        .                                  ⁢                  b          DP                    =              [                                            d                                                                                            e                                      j                    ⁢                                                                                  ⁢                    α                                                  ⁢                d                                                    ]              )    .
Utilizing the assumption that the channel is somewhat sparse, we can capture sufficiently much of the channel energy by only selecting a column subset of BNV,NH(qV, qH). That is, it is sufficient to describe a couple of the SP-beams, which keeps down the feedback overhead. So, we can select a column subset IS consisting of NSP columns of BNV,NH(qV, qH), to create a reduced beam space transformation matrix BIS=[bIS(1) bIS(2) . . . bIS(NSP)]. E.g., one can select columns number IS=[1 5 10 25] to create the reduced beam space transformation matrix BIS=[b1 b5 b10 b25].
The most general precoder structure for precoding of a single layer is given as:
      w    =                            B                      I            s                          ⁡                  [                                                                      c                  1                                                                                                      c                  2                                                                                    ⋮                                                                                      c                                      N                    SP                                                                                ]                    =                                    [                                                                                b                                                                  I                        s                                            ⁡                                              (                        1                        )                                                                                                                                  b                                                                  I                        s                                            ⁡                                              (                        2                        )                                                                                                              …                                                                      b                                                                  I                        s                                            ⁡                                              (                                                  N                          SP                                                )                                                                                                                  ]                    ⁡                      [                                                                                c                    1                                                                                                                    c                    2                                                                                                ⋮                                                                                                  c                                          N                      SP                                                                                            ]                          =                              ∑                          i              =              1                                      N              SP                                ⁢                                    c              i                        ⁢                          b                                                I                  s                                ⁡                                  (                  i                  )                                                                          ,
where {ci}i=1NSP are complex coefficients. A more refined multi-beam precoder structure is achieved by separating the complex coefficients in a power (or amplitude) and a phase part as
  w  =                    B                  I          s                    ⁡              [                                                            c                1                                                                                        c                2                                                                        ⋮                                                                          c                                  N                  SP                                                                    ]              =                            B                      I            s                          ⁡                  [                                                                                                                p                      1                                                        ⁢                                      e                                          j                      ⁢                                                                                          ⁢                                              α                        1                                                                                                                                                                                                            p                      2                                                        ⁢                                      e                                          j                      ⁢                                                                                          ⁢                                              α                        2                                                                                                                                                ⋮                                                                                                                                p                                              N                        SP                                                                              ⁢                                      e                                          j                      ⁢                                                                                          ⁢                                              α                                                  N                          SP                                                                                                                                                  ]                    =                                                  B                              I                s                                      ⁡                          [                                                                                                                  p                        1                                                                                                  0                                                                                                                                                                                                                                                                                            0                                                                                                      p                        2                                                                                                                                                                                                    ⋱                                                                                                                                                                                                                                                                                            ⋱                                                        0                                                                                                                                                                                          ⋱                                                        0                                                                                                      p                                                  N                          SP                                                                                                                                ]                                ⁡                      [                                                                                e                                          j                      ⁢                                                                                          ⁢                                              α                        1                                                                                                                                                              e                                          j                      ⁢                                                                                          ⁢                                              α                        2                                                                                                                                          ⋮                                                                                                  e                                          j                      ⁢                                                                                          ⁢                                              α                                                  N                          SP                                                                                                                                          ]                          =                              B                          I              s                                ⁢                                    P                        ⁡                          [                                                                                          e                                              j                        ⁢                                                                                                  ⁢                                                  α                          1                                                                                                                                                                                e                                              j                        ⁢                                                                                                  ⁢                                                  α                          2                                                                                                                                                          ⋮                                                                                                              e                                              j                        ⁢                                                                                                  ⁢                                                  α                                                      N                            SP                                                                                                                                                          ]                                          
The precoder vector may then be expressed as
  w  =                                          B                          I              s                                ⁢                      P                                    ︸                      =                          W              1                                          ⁢                        [                                                                      e                                      j                    ⁢                                                                                  ⁢                                          α                      1                                                                                                                                            e                                      j                    ⁢                                                                                  ⁢                                          α                      2                                                                                                                          ⋮                                                                                      e                                      j                    ⁢                                                                                  ⁢                                          α                                              N                        SP                                                                                                                          ]                          ︸                      =                          W              2                                            =                  W        1            ⁢                        W          2                .            The selection of W1 may then be made on a wideband basis while the selection of W2 may be made on a subband basis. The precoder vector for subband 1 may be expressed as wl=W1W2(l). That is, only w2 is a function of the subband index 1.
As multiplying the precoder vector w with a complex constant C does not change its beamforming properties (as only the phase and amplitude relative to the other single-polarized beams is of importance), one may without loss of generality assume that the coefficients corresponding to e.g. SP-beam 1 is fixed to pt=1 and ejα1=1, so that parameters for one less beam needs to be signaled from the wireless device to the base station. Furthermore, the precoder may be further assumed to be multiplied with a normalization factor, so that e.g. a sum power constraint is fulfilled, i.e. that is ∥w∥2=1. Any such normalization factor is omitted from the equations herein for clarity.
What needs to be fed back by the wireless device to the base station is thus the chosen columns of BNV,NH(qV, qH), i.e. the NSP single-polarized beams. This requires at most NSp·log2 2NVNH bits.
The vertical and horizontal DFT basis rotation factors qV and qH. For instance, the
            q      ⁡              (        i        )              =          i      Q        ,i=0, 1, . . . , Q−1, for some value of Q. The corresponding overhead would then be 2·log2 Q bits.
The (relative) power levels {p2, p3, . . . , pNSP} of the SP-beams. If L is the number of possible discrete power levels, (NSP−1)·log2 L bits are needed to feed back the SP-beam power levels.
The co-phasing factors
  {            e              j        ⁢                                  ⁢                  α          2                      ,          e              j        ⁢                                  ⁢                  α          3                      ,    …    ⁢                  ,          e              j        ⁢                                  ⁢                  α                      N            SP                                }of the SP-beams. For instance,
            α      ⁡              (        k        )              =                  2        ⁢                                  ⁢        π        ⁢                                  ⁢        k            K        ,k=0, 1, . . . , K−1, for some value of K. The corresponding overhead would be, (NSP−1)·log2 K bits per rank per W2 report.
In some implementations, the phases of the SP-beams may be quantized across frequency. We assume that a multi-beam precoder vector wf for each PRB f=0, 1, . . . , NRB−1 should be quantized and fed back and that the multi-beam precoder vector is a function of the SP-beam phases as
      w    f    =            B              I        s              ⁢                            P                ⁡                  [                                                                      e                                      j                    ⁢                                                                                  ⁢                                                                  α                        1                                            ⁡                                              (                        f                        )                                                                                                                                                                  e                                      j                    ⁢                                                                                  ⁢                                                                  α                        2                                            ⁡                                              (                        f                        )                                                                                                                                                ⋮                                                                                      e                                      j                    ⁢                                                                                  ⁢                                                                  α                                                  N                          SP                                                                    ⁡                                              (                        f                        )                                                                                                                          ]                    .      Note here again that one may set ejα1(f)=1 as only the relative phases are important. We are interested in characterizing the phase change over frequency for each SP-beam, that is, the vectors ϕi=[ejαi(0) ejαi(1) . . . ejαi(NRB−1)]T, i=2, 3, . . . , NSP.
Existing solutions for MU-MIMO based on implicit CSI reports with DFT-based precoders have problems with accurately estimating and reducing the interference between co-scheduled users, leading to poor MU-MIMO performance.
Multi-beam precoder schemes, such as the one presented previously, may lead to better MU-MIMO performance. However, these precoder schemes are designed for Class A type of operation with non-precoded CSI-RS. It is an open question how precoder design for Class B type of operation with beamformed CSI-RS should be done, especially considering when used in a Hybrid Class A/B fashion.